Abstract: Both biologists and economists are concerned about invasive species. There are several well-documented instances in which biological invaders have done extensive damage. This has led some economists to conclude that biological invaders should be treated as a form of "pollution", and that the activity generating the "pollution" international trade should be taxed to the point at which its marginal benefits balance its marginal costs. This prescription presumes a convex objective, however, and this assumption may not hold. If the expected damage done by a biological invader is the damage caused in the event an invasion occurs times the probability of invasion, and the probability of invasion is necessarily bounded by one, there may be situations in which fighting potential invaders is a lost cause and should be abandoned. A simple model illustrates that such results can arise even when potential damages are significant. In general the optimal policy is discontinuous in the magnitude of potential damages. For low-to-medium levels of damage it is best essentially to do nothing to prevent invasion, but at a certain threshold level of potential damages there is a discontinuous policy response from doing nothing to adopting aggressive measures. The dividing line between laissez faire and aggressive responses is associated with the relationship between gains from trade and potential damages. For potential damages in excess of the maximum potential gains from trade aggressive responses are generally warranted, while damages below that threshold often do not merit intervention. These results point to the need to better understand the true costs of biological invasion. It is especially important to distinguish between tangible and intangible values and decide what weight society assigns to the latter.